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A264264 The length of the shortest nontrivial integral cevian of an isosceles triangle, with base of length 1 and legs of length n, that divides the base into two integral parts. 2
4, 9, 6, 9, 36, 11, 14, 81, 16, 19, 30, 15, 24, 225, 26, 19, 48, 31, 34, 441, 36, 39, 84, 35, 44, 69, 32, 49, 900, 51, 34, 87, 56, 59, 1296, 61, 40, 141, 66, 69, 108, 49, 74, 159, 64, 53, 126, 81, 84, 2601, 86, 89, 2916, 91, 94, 147, 66, 61, 66, 101, 70, 165 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
A nontrivial cevian is one that does not coincide with a side of the triangle.
For all n, the longest nontrivial integral cevian has length n^2.
LINKS
Wikipedia, Cevian
EXAMPLE
a(4) = 6 because for legs of length 4 there are two cevians, of length 6 and 16, that divide the base into two integral parts.
PROG
(PARI)
ceviso(n) = {
my(d, L=List());
for(k=1, n^2,
if(issquare(n^2+k^2-k, &d) && d!=n,
listput(L, d)
)
);
Vec(L)
}
vector(100, n, n++; ceviso(n)[1])
CROSSREFS
Cf. A264263.
Sequence in context: A094243 A155875 A105274 * A089390 A053667 A218072
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Nov 10 2015
STATUS
approved

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Last modified April 12 16:49 EDT 2024. Contains 371635 sequences. (Running on oeis4.)